[1]}, [2]}  A finite game \(G\in {\mathcal {G}}_{[n;k_1,\cdots ,k_n]}\)  is a potential game, if and only if the potential equation (REF ) has solution. Moreover, if \(\xi \)  is a solution then the potential function can be expressed as
\(P(x_1,\cdots ,x_n)=V^P\ltimes _{j=1}^nx_j,\) 
